PreprintCC BY 4.0HAL
A unified floor identity for sums of k-th roots
Abstract
We prove that
for all n beyond an explicit bound, for any non-negative integers x i not all equal. This unifies and extends the generalizations of Ramanujan's identity √ n + √ n + 1 = √ 4n + 2 due to Somu and Kukla, and removes the arithmetic hypothesis of one of them.
Related
- Small sums of roots of unity: polylogarithmic exceptional sets and conditional separation
- A detectability floor for treatment-response labels in rheumatology transcriptomics
- On the Euler transform and the floor function
- Floor-crossing for Legendrian Clasp Move
- A combinatorial criterion for detecting roots of Bernstein-Sato polynomials
BibTeX
@misc{mittou2026unified,
title = {{A unified floor identity for sums of k-th roots}},
author = {Brahim Mittou},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05840018v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A unified floor identity for sums of k-th roots
AU - Brahim Mittou
PY - 2026
DA - 2026/10/26
PB - HAL
UR - https://hal.science/hal-05840018v1
AB - We prove that for all n beyond an explicit bound, for any non-negative integers x i not all equal. This unifies and extends the generalizations of Ramanujan's identity √ n + √ n + 1 = √ 4n + 2 due to Somu and Kukla, and removes the arithmetic hypothesis of one of them.
ER -